No bulk thermal currents in massive Dirac fermions

TL;DR

This paper demonstrates that massive Dirac fermions in (2+1) dimensions do not support a bulk thermal Hall current at low temperatures, with heat transport confined to domain wall states, clarifying previous conflicting results.

Contribution

It provides a rigorous calculation showing the absence of bulk thermal Hall currents in massive Dirac fermions, resolving prior controversies and correcting earlier perturbative findings.

Findings

Bulk thermal Hall current is absent at low temperatures.

Thermal transport occurs only along domain walls.

Clarifies and corrects previous perturbative results.

Abstract

We calculate the energy current flowing in the bulk of a (2+1)-dimensional system of massive Dirac fermions and along a (1+1)-dimensional domain wall generated by flipping the sign of the particle mass. We show that, at low temperatures and in the long-wavelenghth limit, the system does not support a bulk thermal Hall current proportional to the temperature gradient. The only such contribution is due to states localised at the domain wall. This puts an end to a controversy existing in the literature and amends previous results obtained via first-order perturbation calculations.